Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...

the rupture, although this region is mostly to the hanging wall side of a projection of the
rupture to the surface (i.e. on the hanging wall of the fault, but the foot wall side of the
rupture). It seams reasonable that there should be some increased motion in this area for a
buried fault.
1-Rjb/Rcld
1.2
1
0.8
0.6
0.4
0.2
0
-40 -20 0 20 40 60 80 100 120
x (line 1) or y (lines 2 and 3)
Line 1 (y=0)
Line 2 (x=3)
Line 3 (x=10)
Figure 17: Variation of the term [ 1−
RJB
/ RRUP
] with location for the three lines shown on Figure
15. Top of rupture is at a depth of 5 km at x=0.
The effectiveness of the term [ 1−
RJB
/ RRUP
] to capture the hanging wall effect was tested by
fitting the selected PEER-NGA data for peak acceleration with a regression model without a
hanging wall term. The residuals were found to be correlated with [ 1−
RJB
/ RRUP
] with a p-
n
value of 0.0024. Exploratory analysis indicated that the model [ 1−
R JB / RRUP
] with n equal
to 2 and ½ produced poorer fits to the data (larger standard error) than a linear model (n= 1).
No significant difference between normal and reverse faulting data was found (p value of
0.63 for adding a normal fault difference in the correlation). The behavior of the residuals
with respect to [ 1−
RJB
/ RRUP
] was checked by separately fitting the data on the hanging
wall, 60º ≤ θSITE ≤ 120º, and footwall, -60º ≤ θSITE ≤ -120º sides of the rupture, excluding
sites directly above the rupture (RJB=0). Figure 18 shows the residuals and linear fits with
respect to [ 1−
RJB
/ RRUP
] constrained to go through 0 at [ 1−
RJB
/ RRUP]
=0. The solid lines
show the mean trend and the dashed lines the 90% confidence interval for the mean. The
residuals on the hanging wall and footwall side of the ruptures have essentially identical
trends.
Previous empirical models (Abrahamson and Silva, 1997; Campbell and Bozorgnia, 2003)
have limited the hanging wall effect to faults with dip angles, δ, less than 70º. Assuming the
hanging wall effect is a geometric effect, one might expect that it might correlate with δ.
Figure 19 shows residuals for sites on the hanging wall of reverse faults (RJB = 0) plotted
versus δ. The data indicate increasing motion with decreasing δ. The trend was modeled
with linear functions with 90º - δ, cos(δ) and cos 2 (δ). All three functions show a significant
trend with the residuals, with cos 2 (δ) providing a slightly better fit than the other two models.
Similar results were found including data from sites with [ 1−
RJB
/ RRUP]
> 0.8 and for data
from sites with RJB < 5 km.
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